What is the derivative of 3^{2x^2} ?

The derivative of 3^{2x^2} is 4ln(3)*9^{x^2}x

What is the first derivative of 3^{2x^2} ?

The first derivative of 3^{2x^2} is 4ln(3)*9^{x^2}x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (3^{2 x^{2}})

4 ln (3) \cdot 9^{x^{2}} x

Solution steps

\frac{d}{d x} (3^{2 x^{2}})

Simplify

3^{2 x^{2}} : 9^{x^{2}}

= \frac{d}{d x} (9^{x^{2}})

Apply exponent rule:

a^{b} = e^{b l n (a)}

9^{x^{2}} = e^{x^{2} l n (9)}

= \frac{d}{d x} (e^{x^{2} l n (9)})

Apply the chain rule:

e^{x^{2} l n (9)} \frac{d}{d x} (x^{2} ln (9))

= e^{x^{2} l n (9)} \frac{d}{d x} (x^{2} ln (9))

\frac{d}{d x} (x^{2} ln (9)) = 4 ln (3) x

= e^{x^{2} l n (9)} \cdot 4 ln (3) x

e^{x^{2} l n (9)} = 9^{x^{2}}

= 4 ln (3) \cdot 9^{x^{2}} x

What is the derivative of 3^{2x^2} ?
The derivative of 3^{2x^2} is 4ln(3)*9^{x^2}x
What is the first derivative of 3^{2x^2} ?
The first derivative of 3^{2x^2} is 4ln(3)*9^{x^2}x